Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, September 28, 2023, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Yanheng Wang

Continuity of Exact Perfect Matchings

Given a graph whose edges are either red or blue, a perfect matching is dubbed a k-PM if it contains exactly k reds. Generally the existence of 3-PM and 7-PM, say, tells us nothing about the existence of k-PM for k=4,5,6. In fact the feasibility regime can be as fractured as you want, hence "discontinuous". This talk goes in the other direction: We investigate for which graphs, and to what extent, does the feasibility of k-PM exhibit continuity. Several such graphs were known previously, for example graphs of small independence number [El Maalouly and Steiner 2022] and doubly chordal graphs [Haslebacher 2023]. I will summarise them under the "sandwich paradigm" which already appeared in former works. Then we apply the paradigm on some other graphs, notably those of small modular width. I will also sketch some "lifting theorems" saying that certain graphs can be "blown up" without breaking continuity. The talk is based on my thesis supervised by Bernd Gärtner and Nicolas El Maalouly.

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